MathDBThe MMS star conjecture for Latin squares of order 6
The MMS star conjecture for Latin squares of order 6
A Latin square of order can be viewed as the corresponding orthogonal-array configuration, with points and lines carrying the induced incidence structure. It has the MMS star property when, for every zero-sum weighting of its points, the largest set of nonnegative lines has size at least the size of a star.
MMS star conjecture for order 6. Any Latin square of order has the MMS star property.
The authors state this after noting that they have no examples with a weighting having only nonnegative lines. The source gives no proof or disproof, so the conjecture remains open.
Sources & referencesView supporting material
Primary source
Ferdinand Ihringer and Karen Meagher, “Manickam-Miklós-Singhi Conjectures on Partial Geometries”, arXiv:1606.06275 (2017).
Progress summary
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